Combine oil, lemon juice, syrup, miso (if using), garlic, pepper, and ¾ teaspoon salt in a jar. Cover tightly with lid and shake well.
Toss radicchio and arugula with half of dressing (about ½ cup) and ½ teaspoon salt in a large bowl. Transfer leaves to a serving platter.
Add beets to bowl; toss with ¼ cup dressing and remaining ¼ teaspoon salt. Arrange beets on top of leaves. Top with oranges and drizzle with remaining ¼ cup dressing. Sprinkle with cheese and pistachios.
